Well-posedness and blowup of the geophysical boundary layer problem

Under the assumption that the initial velocity and outflow velocity are analytic in the horizontal variable, the local well-posedness of the geophysical boundary layer problem is obtained by using energy method in the weighted Chemin-Lerner spaces. Moreover, when the initial velocity and outflow velocity satisfy certain condition on a transversal plane, it is proved that the $W^{1,\infty}-$norm of any smooth solution decaying exponentially in the normal variable to the geophysical boundary layer problem blows up in a finite time.